Consider
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
In Python's view, x has shape (4, 3) and v shape (3, ). Why didn't Python view v as having shape (, 3). Also, why do v and v.T have the same shape (3, ). IMHO, I think if v has shape (3, ) then v.T should have shape (, 3)?
(3,) does not mean the 3 is first. It is simply the Python way of writing a 1-element tuple. If the shape were a list instead, it would be [3].
(, 3) is not valid Python. The syntax for a 1-element tuple is (element,).
The reason it can't be just (3) is that Python simply views the parentheses as a grouping construct, meaning (3) is interpreted as 3, an integer.
x.shape as (4, 3), it would be more intuitive/consistent to show v.shape as (1, 3) and v.T.shape as (3, 1)?
v is one dimensional, meaning len(v.shape) should be nothing else other than 1.As you know, numpy arrays are n-dimensional. The shape tells dimensions in the order. If it is 1-D you will see only 1st dimension, 2-D only 2 dimensions and so on.
Here x is a 2-D array while v is a 1-D array (aka vector). That is why when you do shape on v you see (3,) meaning it has only one dimension whereas x.shape gives (4,3). When you transpose v, then that is also a 1-D array. To understand this better, try another example. Create a 3-D array.
z=np.ones((5,6,7))
z.shape
print (z)
v.T.shape as (, 3) which both conform to v.T as one dimension and make distinction between v and v.T. Although Tomothy explained the syntax is (elements, ) but why can't it be (, elments)?
v and v.T are both 1-D. But my wish was that Python should have shape (3, ) and (, 3) respectively to make things more intuitive!
shapeis atuple), and what does it mean to be 1 dimensional. People coming from MATLAB, and some linear algebra, backgrounds, can't conceive of an array that only has 1 dimension. It has to be a row vector or column vector, never a plain vector. :)